The degree profile of Pólya trees

Details The degree profile of Pólya trees The degree profile of Pólya trees

2011-04-21

arxiv.org/abs/1104.4271v1

Mathematics

Combinatorics

31 pages, 3 figures

Scientific paper

We investigate the profile of random P\'olya trees of size $n$ when only nodes of degree $d$ are counted in each level. It is shown that, as in the case where all nodes contribute to the profile, the suitably normalized profile process converges weakly to a Brownian excursion local time. Moreover, we investigate the joint distribution of the number of nodes of degree $d_1$ and $d_2$ in the levels of the tree.

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